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The Power Series

  1. Mar 21, 2010 #1
    I just had this question on my exam and I was wondering whether my method of calculating it was right:

    I was meant to find sum to n terms of this:

    1, (4-a)x, (7-a^2)x^2, (10-a^3)x^3, (13-a^4)x^4........

    Would the correct way to go about it be expand it:

    1, 4x-ax. 7x^2-a^2x^2.....

    and then it would be:

    Sn = (power series of 1, 4x, 7x^2.....) - ax(1-ax^(n-1)/(1-ax)
     
  2. jcsd
  3. Mar 21, 2010 #2

    tiny-tim

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    Hi Procrastinate! :smile:

    (try using the X2 tag just above the Reply box :wink:)

    The first thing to do with any question like this (in my opinion, anyway) is to write it logically …

    it's ∑ (3n + 1 - an)xn

    = ∑ xn + 3∑ nxn - ∑(ax)n:wink:
     
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